MoDisc User`s Manual
Contents
1. was generated from Model 1 with noise representing experimental error added Both models were simulated via ordinary differential equations where parameters were fitted to the experimental data Time represented by t was the independent variable Simulation and experimental results were entered into an Excel file shown in Figure 1 Such a file may be used as an input file for the MoDisc program Note that replicate experimental results were also included MoDisc was then used to calculate which of these two models was most probable In this case the first model was selected as most probable with a probability share of 0 65 The probability share of the second model was 0 35 This result should not be surprising given that the experimental data was generated artificially from Model 1 to begin with It should additionally be pointed out that although only two models were compared in this particular case any number of models may be compared in actuality 3 44 MoDisc In Action A Reaction Kinetics Example 3 MODISC USAGE 090e M ExampleSystem txt gt A B c I D _1 begin comment _2 Example System _3 The comments may have multiple lines of text _4 This is a good place for recording information related _5 tothe runs and the experiment 6 end comment S75 _8 9 _10 begin model model 1 _11 parameters 2 _12 variables 4 13 dof 6 14 t al a2 a3 AS 0 5 0 901 0 087 0 011 _16 1 0 812 0 146 0 041 17 2 0 62. of the principal points are provided here Stewart s Method is based on calculating the posterior probabilities of competing models relative to each other The model with highest probability is considered the most likely choice relative to the other models Calculation of posterior probabilities are based on the following proportionality Pj Ve p M Y x p Mj 2 77 1 where M is the jt model Y is the matrix of experimental results and p M Y is the posterior probability of model M given Y Additionally p is the number of independent parameters Ve is the number of degrees of freedom and is the determinant function The elements of the determinant function are given by 3 MODISC USAGE Vik O3 Nu1lYiu Fiil u 05 Y ku Fin Eur 03 i j 1 2 in which n is the the total number of events evaluated q is the number of different chemical species monitored and F 8 is the model prediction is the vector of the number of different independent conditions i e temperature tested and O is the vector of parameters providing the best fit of the model to the experimental data Normalizing the results of Equation 1 for any given model to the sum of the results for all the models is referred to as the probability share and is shown in Equation 3 p M Y TE Mil Y es a Y p My Y k 3 The model with the highest probability share is considered most probable 3 MoDis
3. 3 3 Running MoDisc To run MoDisc first launch LispWorks Under the LispWorks menu bar choose File Open and select the modisc lsp file This will result in an editor window being launched containing the modisc source code Select the editor window using your mouse Then go to the menu bar and select Buffers Compile Finally at the CL USER 1 gt prompt in the original Lisp Works window type modisc make sure to include the parenthesis At this point you will be prompted for your input file After reading the input file in MoDisc will return the probability share of each of the models 3 44 MoDisc In Action A Reaction Kinetics Example 3 MODISC USAGE 3 4 MoDisc In Action A Reaction Kinetics Example A reaction kinetics example adapted from 5 using two different models is provided here In this example it is known that the system consists of three chemical species a1 a2 and a3 However the exact reaction mechanism is not known and two hypotheses are put forward In the first proposed reaction scheme Model 1 it hypothesized that the chemical species a1 a2 and a3 follow a series of sequential irreversible reactions as represented by al amp a2 B a3 4 The second proposed model Model 2 is similar to Model 1 However in this case all the reactions are considered to be reversible ky ka al a2 a3 5 k3 ka In this example for the sake of illustration the experimental data
4. 6 0 208 0 131 18 4 0 435 0 215 0 349 19 8 0 19 0 123 0 686 _20 16 0 036 0 026 0 938 _21 end model 22 23 begin model model 2 _24 parameters 4 _25 variables 4 _26 dof 6 27 t al a2 a3 28 a5 0 899 0 089 0 011 29 1 0 809 0 15 0 041 30 2 0 656 0 211 0 132 31 4 0 434 0 216 0 35 _32 8 0 191 0 123 0 685 33 16 0 037 0 026 0 936 34 end model 35 _36 begin experiment 37 variables 4 38it ai a2 a3 39 0 5 0 959 0 025 0 028 40 0 5 0 914 0 061 0 41 1 0 855 0 152 0 068 _42 1 0 785 0 197 0 096 43 2 0 628 0 13 0 09 44 2 0 617 0 249 0 118 45 4 0 48 0 184 0 374 46 4 0 423 0 298 0 358 47 8 0 166 0 147 0 651 48 8 0 205 0 5 0 684 49 16 0 034 o 0 899 50 16 0 054 0 047 0 991 _51 end experiment 52 ExampleSystem txt Figure 1 Model results and experimental data for MoDisc may be entered via a spread sheet A reaction kinetics example using two different models is shown here and described in detail in Section 3 4 Note that more than two models at a time may be compared REFERENCES REFERENCES References 1 R Jain A L Knorr J Bernacki and R Srivastava Investigation of Bacteriophage MS2 Vi ral Dynamics Using Model Discrimination Analysis and the Implications for Phage Therapy Biotechnol Prog 22 6 1650 8 2006 2 A L Knorr R Jain and R Srivastava Bayesian based selection of metabolic objective func tions Bioinformatics 23 3 351 357 2007 3 A L Knorr and R Srivastava Evaluat
5. MoDisc User s Manual Ranjan Srivastava Ph D Last modified June 11 2007 1 Summary 2 Overview 21 so eo af ws Soe Ge ah Ge al we we wk wR He en Ge Bw bi Ge ww a we U 2 2 Model Discommaton Thecty cios ce cres daa A A cada 3 MoDisc Usage 31 Software Installation oa ae hw ee He a PR eae a a EEG A See A yong ee a te Se we eB ee eh oe a ae ard 33 Running MoDise ome ba bh A SY Ee eS 3 4 MoDisc In Action A Reaction Kinetics Example 1 SUMMARY 1 Summary MoDisc is a Bayesian based model discrimination application for the identification of the most probable model out of a pool of models given a set of experimental data MoDisc does not carry out simulations Rather it allows analysis of simulation results that have already been generated in conjunction with experimental data to evaluate model quality As an example of a typical usage of MoDisc consider a researcher who is studying signal trans duction systems in some organism Assume that researcher postulated three different hypotheses regarding the signaling mechanism Further assume that the researched had collected some experi mental data about the process but not enough to definitively identify which hypothesis was correct In such a scenario the researcher might use MoDisc to help evaluate the most probable hypothesis in the following manner First the researcher would need to translate his or her hypotheses into some kind of mathematical model
6. c Usage 3 1 Software Installation To carry out installation of MoDisc it is first necessary to download and install the LispWorks Common Lisp Personal Edition software The software may be freely downloaded from http www lispworks com downloads index html along with documentation of how to install the soft ware LispWorks is available for Windows Linux and OS X Once the LispWorks Personal Edition is installed the MoDisc code may be downloaded MoDisc is available at http www engr uconn edu srivasta modisc html The link for the software is found on the left hand side menu bar You may also directly download it from http www engr uconn edu srivasta modisc html modisc zip Why Lisp For those with experience with various mathematical software packages such as Math ematica or MATLAB one might ask Why not implement MoDisc in one of those languages The reason is simple We wanted to make this tool available to as large a group as possible Other packages such as those already mentioned require a license The code we provide may be used after downloading a free copy of the Lispworks Personal Edition A further benefit of the Lisp works platform is that it runs on the three major operating systems Windows Linux and OS X 3 2 Input File 3 MODISC USAGE The reason for using Common Lisp over C Fortran or Java was primarily a matter of preference Overall we felt this was the best way to ensure that the most possible pe
7. gical phenomena several models of a system may be postulated The question then becomes how to discriminate among the models to determine which is most likely A method for identifying the most probable model of a chemical reaction network based on ex perimental data was developed by Stewart and colleagues 4 5 This approach termed model discrimination is a Bayesian based method in which the probability of a model given a set of experimental data may be calculated and compared to other potential models The model with the highest value is considered the most probable model to describe the system Model discrimination has wide applicability for use with biological systems Types of systems that may be analyzed include but are not limited to models of transcriptional regulatory networks intracellular kinetic models or models of viral dynamics 1 3 It should be noted that whether these models are deterministic stochastic or a mixture of both paradigms model discrimination analysis may still be carried out without any hinderance Model discrimination has also found utilization beyond the study of kinetic models Recently this methodology has been used to identify the most probable objective function for use in metabolic flux analysis 2 2 2 Model Discrimination Theory Stewart s Method of model discrimination is based upon Bayesian analysis A full derivation of the technique is provided in 4 and 5 However a brief description
8. ion of HIV 1 kinetic models using quantitative discrimi nation analysis Bioinformatics 21 8 1668 77 2005 4 W E Stewart T L Henson and G E P Box Model Discrimination and Criticism with Single Response Data AIChE Journal 42 11 3055 3062 1996 5 W E Stewart Y Shon and G E P Box Discrimination and goodness of fit of multiresponse mechanistic models AIChE Journal 44 6 1404 1412 1998
9. ople who wanted to use the software actually could use it 3 2 Input File To use MoDisc experimental data and model information may be entered via an input file The file may be in the form of a spreadsheet such as an Excel file such as shown in Figure 1 or as a tab delimited text file The input file is organized into a series of blocks of information for MoDisc The first block is for the comments sections Comments may be entered within a begin comment and end comment section The next set of of blocks are for the details of the model as well as the results of the simulation Model simulation results may be entered by starting a section called begin model followed by the name of the model The number of parameters the number of variables and the number of degree of freedoms are entered next The following row consists of a list of the variables used in the simulation Simulation results for the specific model are then entered Finally the block is closed by ending it with an end model row This procedure is repeated for each of the remaining models To enter the experimental data a new block is started by entering begin experiment in a new row The number of variables are then entered followed by a row consisting of the independent and dependent variables measured Finally the experimental data is entered followed by an end experiment row The file may then be saved as a tab delimited text file
10. such as using a system of ordinary differential equations to de scribe the signaling phenomena Then the researcher would need to carry out parameter estimation for each of the three models based on the collected experimental data as well as any data from the literature that might be usable The next to step would be to carry out simulations using each of the three models and collecting the resulting simulation data At this point the simulation data and the actual experimental data may be fed into MoDisc and the most probable model hypothesis will be determined It is important to note however that MoDisc may be used for far more than just the cell signaling example provided here Types of analyses may range from identification of the most probable kinetic model whether deterministic stochastic or a combination of both to the determination of the most probable objective function for metabolic flux analysis MoDisc is capable of running on the Windows Linux and the OS X platforms Software documentation and updates are freely available at http www engr uconn edu srivasta modisc html 2 OVERVIEW 2 Overview 2 1 Introduction Model development is a useful tool for understanding a wide range of phenomena in the sciences and engineering Within the area of biological sciences this approach is becoming more important as scientists strive to keep up with the rapid influx of data being generated In attempting to make sense of biolo
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